Skip to main content

Implications of Using Mathematical Modelling as a Pedagogical Tool on the Mathematical Concepts of Proportions and Proportional Reasoning in a Non-prototypical Secondary Mathematics Classroom

  • Chapter
Mathematical Modelling Education in East and West

Abstract

Consistent with international trends, mathematical modelling is heralded and has been documented as a construct that is imperative for the teaching and learning of mathematics in South African schools. The study discussed in this chapter explored the immediate implications of using mathematical modelling as a framework for the teaching and learning of powerful mathematical concepts such as proportional reasoning in South African schools located in under-resourced low socio-economic areas. Results show that the initial apprehension that students experienced when exposed for the first time to a model-eliciting activity was soon transformed into a diverse range of creative mathematical approaches, when they learned that the activity is open-ended by default.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Arseven, A. (2015). Mathematical modelling approach in mathematics education. Universal Journal of Education Research, 3(12), 973–980.

    Article  Google Scholar 

  • Borromeo Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM—Mathematics Education, 38(2), 86–95.

    Article  Google Scholar 

  • Department of Basic Education (DBE) (2011). Curriculum and Assessment Policy Statement (CAPS): Mathematics Grades 10–12. Pretoria: Department of Basic Education, South Africa.

    Google Scholar 

  • English, L. D. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54(2), 225–248.

    Article  Google Scholar 

  • Galbraith, P., & Holton, D. (2018). Mathematical modelling: A guidebook for teachers and teams. Retrieved from www.immchallenge.org.au/files/IM2C-Teacher-and-student-guide-to-mathematical-modelling.pdf.

  • Kang, O., & Noh, J. (2012). Teaching mathematical modelling in school mathematics. 12th International Congress on Mathematical Education. 8–15 July 2012, Seoul, Korea. Available from http://www.icme12.org/upload/submission/1930_f.pdf.

  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R., & Lehrer, R. (2003). Models and modelling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129. https://doi.org/10.1080/10986065.2003.9679996.

    Article  Google Scholar 

  • Lesh, R., Zawojewski, J., & Carmona, L. (2003). What mathematical abilities are needed for success beyond school in a technology-based age of information? In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 205–221). Mahwah, NJ: Lawrence Erlbaum Associates.

    Chapter  Google Scholar 

  • Mooney, D., & Swift, R. (1999). A course in mathematical modelling. The Mathematical Association of America. ISBN: 0-88385-712-X.

    Google Scholar 

  • Moreno-Armella, L., & Block, D. (2002). Democratic access to powerful mathematics in a developing country. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 301–321). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A modelling perspective on the teaching and learning of mathematical problem solving, Mathematical Thinking and Learning. 10(3), 293–304. https://doi.org/10.1080/10986060802218132.

  • Pertamawati, L., & Retnowati, E. (2019). Model-Eliciting Activities: Engaging students to make sense of the world. Journal of Physics: Conference Series, 1200(1),  012003. https://doi.org/10.1088/1742-6596/1200/1/012003

    Google Scholar 

  • Schorr, R. Y., & Lesh, R. (2003). A modelling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics teaching, learning, and problem solving (pp. 141–157). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Skovsmose, O., & Valero, P. (2002). Democratic access to powerful mathematical ideas. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 383–407). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Stohlmann, M. S. (2017). Mathematical modelling with middle school students: The robot art model-eliciting activity. European Journal of STEM Education, 2(2), 4. https://doi.org/10.20897/ejsteme.201704.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Muzi Manzini .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Cite this chapter

Manzini, M., Mhakure, D. (2021). Implications of Using Mathematical Modelling as a Pedagogical Tool on the Mathematical Concepts of Proportions and Proportional Reasoning in a Non-prototypical Secondary Mathematics Classroom. In: Leung, F.K.S., Stillman, G.A., Kaiser, G., Wong, K.L. (eds) Mathematical Modelling Education in East and West. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-030-66996-6_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-66996-6_33

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-66995-9

  • Online ISBN: 978-3-030-66996-6

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics